Question

# A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses (in MPa)

A
109.8, 45.2
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B
109.8, 40.2
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C
109.8, 31
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D
109.8, 50
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Solution

## The correct option is B 109.8, 40.2Given : Di = 100 mm, Do = 110 mm, D=105 mm For Thin cylinder J=πDt(D24)=π×105×5×(52.5)2 =4547729mm4=4.547×106mm4 τmax=T×rmaxJ where rmax=Do2=55mm ∴τmax=2000×103×554.547×106=24.20MPa σH=σc=pdi2t=100MPa σL=50MPa σ1′σ2=1502±√252+24.202 =75±34.8=109.8,40.2MPa

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